1. Field of the Invention
This invention relates to quantum computing and to solid state devices that use superconductive materials to create and maintain coherent quantum states such as required for quantum computing.
2. Description of Related Art
Research on what is now called quantum computing traces back to Richard Feynman. See R. Feynman, Int. J. Theor. Phys., 21, 467-488 (1982). Feynman noted that quantum systems are inherently difficult to simulate with conventional computers but that observing the evolution of a quantum system could provide a much faster way to solve some computational problems. In particular, solving a theory for the behavior of a quantum system commonly involves solving a differential equation related to the Hamiltonian of the quantum system. Observing the behavior of the quantum system provides information regarding the solutions to the equation.
Further efforts in quantum computing were initially concentrated on xe2x80x9csoftware developmentxe2x80x9d or building of the formal theory of quantum computing. Milestones in these efforts were the discoveries of the Shor and Grover algorithms. See P. Shor, SIAM J. of Comput., 26:5, 1484-1509 (1997); L. Grover, Proc. 28th STOC, 212-219 (1996); and A. Kitaev, LANL preprint quant-ph/9511026 (1995). In particular, the Shor algorithm permits a quantum computer to factorize natural numbers. Showing that fault-tolerant quantum computation is theoretically possible opened the way for attempts at practical realizations of quantum computers. See E. Knill, R. Laflamme, and W. Zurek, Science, 279, p. 342 (1998).
One proposed application of a quantum computer is factoring of large numbers. In such an application, a quantum computer could render obsolete all existing encryption schemes that use the xe2x80x9cpublic keyxe2x80x9d method. In another application, quantum computers (or even a smaller scale device, a quantum repeater) could enable absolutely safe communication channels, where a message, in principle, cannot be intercepted without being destroyed in the process. See H. J. Briegel et al., LANL preprint quant-ph/9803056 (199) and the references therein.
Quantum computing generally involves initializing the states of N qubits (quantum bits), creating controlled entanglements among the N qubits, allowing the quantum states of the qubits to evolve under the influence of the entanglements, and reading the qubits after they have evolved. A qubit is conventionally a system having two degenerate quantum states, and the state of the qubit can have non-zero probability of being found in either degenerate state. Thus, N qubits can define an initial state that is a combination of 2N states. The entanglements control the evolution of the distinguishable quantum states and define calculations that the evolution of the quantum states performs. This evolution, in effect, can perform 2N simultaneous calculations. Reading the qubits after evolution is complete determines the states of the qubits and the results of the calculations.
Several physical systems have been proposed for the qubits in a quantum computer. One system uses chemicals having degenerate nuclear spin states. Nuclear magnetic resonance (NMR) techniques can read the spin states. These systems have successfully implemented a search algorithm and a number-ordering algorithm. See M. Mosca, R. H. Hansen , and J. A. Jones, xe2x80x9cImplementation of a quantum search algorithm on a quantum computer,xe2x80x9d Nature, 393:344-346, 1998 and Lieven M. K. Vandersypen, Mattias Steffen, Gregory Breyta, Costantino S. Yannoni, Richard Cleve and Isaac L. Chuang, xe2x80x9cExperimental Realization Of Order-Finding With A Quantum Computer,xe2x80x9d LANL preprint quant-ph/0007017 (2000) and the references therein. These search processes are related to the quantum Fourier transform, an essential element of both Shor""s algorithm for factoring of a natural number and Grover""s Search Algorithm for searching unsorted databases. See T. F. Havel, S. S. Somaroo, C.-H. Tseng, and D. G. Cory, xe2x80x9cPrinciples And Demonstrations Of Quantum Information Processing By NMR Spectroscopy,xe2x80x9d 2000 and the references therein, which are hereby incorporated by reference in their entirety. However, efforts to expand such systems up to a commercially useful number of qubits face difficult challenges.
Another physical system for implementing a qubit includes a superconducting reservoir, a superconducting island, and a dirty Josephson junction that can transmit a Cooper pair (of electrons) from the reservoir into the island. The island has two degenerate states. One state is electrically neutral, but the other state has an extra Cooper pair on the island. A problem with this system is that the charge of the island in the state having the extra Cooper pair causes long range electric interactions that interfere with the coherence of the state of the qubit. The electric interactions can force the island into a state that definitely has or lacks an extra Cooper pair. Accordingly, the electric interactions can end the evolution of the state before calculations are complete or qubits are read. This phenomenon is commonly referred to as collapsing the wavefunction, loss of coherence, or decoherence. See xe2x80x9cCoherent Control Of Macroscopic Quantum States In A Single-Cooper-Pair Box,xe2x80x9d Y. Nakamura; Yu, A. Pashkin and J. S. Tsai, Nature Volume 398 Number 6730 Page 786-788 (1999) and the references therein.
Another physical system for implementing a qubit includes a radio frequency superconducting quantum interference device (RF-SQUID). See J. E. Mooij, T. P. Orlando, L. Levitov, Lin Tian, Caspar H. van der Wal, and Seth Lloyd, xe2x80x9cJosephson Persistent-Current Qubit,xe2x80x9d Science Aug. 13, 1999; 285: 1036-1039, and the references therein, which are hereby incorporated by reference in their entirety. The RF-SQUID""s energy levels correspond to differing amounts of magnetic flux threading the SQUID ring. Application of a static magnetic field normal to the SQUID ring may bring two of these energy levels, corresponding to different magnetic fluxes threading the ring, into resonance. Typically, external AC magnetic fields can also be applied to pump the system into excited states so as to maximize the tunneling frequency between qubit basis states. A problem with this system is that the basis states used are not naturally degenerate and the biasing field required has to be extremely precise. This biasing is possible for one qubit, but with several qubits, fine tuning this bias field becomes extremely difficult. Another problem is that the basis states used are typically not the ground states of the system but higher energy states populated by external pumping. This requires the addition of an AC field-generating device, whose frequency will differ for each qubit as the individual qubit parameters vary.
Research is continuing and seeking a structure that implements a quantum computer having a sufficient number of qubits to perform useful calculations.
In accordance with one embodiment of the invention, a qubit includes a dot formed of a superconductor having a pairing symmetry that contains a dominant component with non-zero angular momentum, and a subdominant component that can have any pairing symmetry. The high temperature superconductors YBa2Cu3O7xe2x88x92x, Bi2Sr2Canxe2x88x921CunO2n+4, Tl2Ba2CuO6+x, and HgBa2CuO4, are examples of superconductors that have non-zero angular momentum (dominant d-wave pairing symmetry), whereas the low temperature superconductor Sr2RuO4, or the heavy fermion material CeIrIn5, are examples of p-wave superconductors that also have non-zero angular momentum.
In such qubits, persistent equilibrium currents arise near the outer boundary of the superconducting dot. These equilibrium currents have two degenerate ground states that are related by time-reversal symmetry. One of the ground states corresponds to persistent currents circulating in a clockwise fashion around the superconducting dot, while the other ground state corresponds to persistent currents circulating counter-clockwise around the dot. The circulating currents induce magnetic fluxes and therefore magnetic moments, which point in opposite directions according to the direction of current flow in the dot, and the magnetic moments may be used to distinguish the states of the qubit.
In accordance with another embodiment of the invention, a qubit includes a superconductive film or bulk superconductor, in which a region of the superconductive material has been removed or damaged. This region is sometimes referred to herein as an xe2x80x9canti-dotxe2x80x9d. The superconductive film or bulk surrounding the anti-dot or region of removed or damaged superconductor supports two degenerate ground states corresponding to equilibrium persistent currents circulating in clockwise and counter-clockwise directions around the anti-dot. These two states may be distinguished by the magnetic moments that they produce.
In accordance with yet another embodiment of the invention, a qubit includes a material such as YBa2Cu3O7xe2x88x92x, which can undergo an insulating-superconducting transition and when in the insulating state can be locally turned superconducting through photon or particle irradiation. This material is prepared in the insulating state, for example, in the anti-ferromagnetic insulating state of YBa2Cu3O7xe2x88x92x, which requires x to be strictly greater than 0.6, and strictly less than 1. This insulator is then irradiated, for example using scanning near field microscopy. The irradiation turns a region superconducting to create a superconducting dot or anti-dot in the parent insulator. This dot or anti-dot then gives rise to persistent equilibrium currents at the boundary between the superconducting area and the insulating background. These currents give rise to two nearly degenerate ground states, which correspond to clockwise and counterclockwise current circulation around the dot or anti-dot. The magnetic moments created by these current flows distinguish the two degenerate states.
To write to (or initialize the state of) a dot or anti-dot qubit, a static magnetic field having a magnitude that depends on the qubit""s structure, is applied normal to the plane of the qubit and in a direction chosen according to the desired basis state (|0 greater than  or |1 greater than ). The magnetic field breaks the energy degeneracy of the qubit states. With this bias, the qubit will decay to the most energetically favorable state (either |0 greater than  or |1 greater than  as required), with the time to decay typically being shorter than 1 millisecond but depending on the chosen embodiment of the invention.
To perform single qubit operations on a dot or anti-dot qubit, an external magnetic field applied to the qubit can be modulated. Application of a magnetic field in the plane of the qubit generates a term in the effective Hamiltonian of the form xcex94(Hx){circumflex over ("sgr")}x, where the tunneling matrix element xcex94(Hx) between the states can be varied over a large range, typically from zero (for zero transverse field) to 100 GHz depending on the specific embodiment of the qubit. Applying a magnetic field normal to the plane of the qubit provides a term proportional to {circumflex over ("sgr")}z,
To overcome the effects of tunneling and remain in a specific state, an alternating magnetic field B(t) normal to the qubit can be used. This has the effect of adding to the Hamiltonian a term proportional to B(t){circumflex over ("sgr")}z where, for example, B(t) can be a square wave. This method is also used in conjunction with a clock whose frequency is an integer multiple of the square wave frequency (so that at every clock pulse, the qubit is in the same state in which it began).
To read from the qubit, any ultra-sensitive instrument that reads sub-flux-quantum level magnetic fields, such as a SQUID microscope or magnetic force microscope, can determine the direction of the magnetic flux and thereby read the supercurrent state associated with the dot or anti-dot.
In accordance with an embodiment of the invention, a quantum computing method cools a structure including a plurality of independent qubits to a temperature that makes the relevant systems superconducting and suppresses the decoherence processes in the system. After the structure is at the appropriate temperature, the method establishes a circulating supercurrent in each qubit in a quantum state that can be an admixture of a first state having a first magnetic moment and a second state having a second magnetic moment. The supercurrent in each qubit is a ground state current arising from use of a superconductor with a dominant order parameter having non-zero angular momentum and a subdominant order parameter having any pairing symmetry. Applying the magnetic bias fields normal to the plane of the qubits can set the state of the current. The quantum state evolves according to probabilities for tunneling between the two ground states in the presence of an externally applied magnetic field. Measuring a magnetic moment or flux due to the supercurrent generated by the qubit determines a result from the quantum evolution.